Digital to analog circuits, like their counterpart analog to digital circuits, are used to provide interfaces between digital circuits and analog circuits. In digital circuits, processing is performed in connection with digital data words. Each data word comprises a predetermined number of data bits, and may represent, for example, a numerical value in connection with which processing, such as the performance of mathematical operations, may occur. Each data bit is represented by an electrical signal which may have predetermined voltage characteristics each representing one of the plurality of digital values that the bit may have. Typically, the precision with which a digital circuit can process digital data depends on the number of data bits provided by the circuit. Accordingly, if a circuit designer determines that a digital circuit requires additional precision, it is a relatively simple matter to add the circuitry to handle the additional bits that may be required to be processed.
In analog circuits, however, processing is performed in connection with the voltage or current levels of one or more input signals, which may represent data. Generally, analog circuits may process the data faster that a digital circuit might. However, the precision of an analog circuit is limited by the precision of the various electrical components, such as resistors, inductors, capacitors, and so forth, of which it is made, and analog circuits typically can process data at a somewhat lower precision than a digital circuit.
Digital processing has other advantages over analog, however, particularly in that words of digital data can be stored for long periods of time, whereas the storage of analog signals generally is limited to a relatively short length of time before its current or voltage level dissipates.
However, in many instances, analog circuitry is required. For example, data in scientific experiments is initially in analog form, and data acquisition circuitry must be able to capture it using analog circuitry. At some point, the data may be converted to digital form for storage and further processing. In addition, it is often convenient to display data, which has been processed in digital form, in analog form using a visual display, to give an observer a visual representation of the processed data. Interfaces between analog and digital systems are required in such instances.
Several basic types of digital to analog converter circuits are known, as is generally described in, for example, J. Millman, Microelectronics: Digital and Analog Circuits And Systems (New York: McGraw-Hill Book Company, 1979) at pp. 606-609. Generally, digital to analog converter circuits include an operational amplifier that amplifies a voltage at an input terminal, which voltage it receives from a resistor network. The resistor network is generally connected to two distinct reference voltages, one of them typically a ground voltage and receives a number of signals, each representative of the condition of bits of the digital word being "converted." The conditions of the diverse bits of the digital word effectively control selected ones of the resistors to connect resistors to one of the two reference voltages. If the resistance values of the resistors forming the resistor network could be made perfect, which could be quite expensive, changes in the numerical value of the digital word controlling the resistor network would result in a proportional change in the voltage applied to the input terminal of the operational amplifier and thus a proportional change in its output voltage level. However, manufacturing variations of the resistors used in implementing an actual digital to analog converter circuit of reasonable cost result in some tolerance in their actual resistor values, in which case changes in voltage levels generated by a digital to analog converter do not necessarily change in direct proportion to changes in the values of the digital word applied thereto. Indeed, the variations in resistance values may, in an actual circuit, be sufficiently large that changes in voltage levels may not be monotonic with changes from one value of the digital word to the next higher or lower value.